A Novel State Decomposition-Based Privacy-Preserving Algorithm for Distributed Optimization over Directed Networks

With the widespread application of distributed optimization, various of algorithms have been developed. However, the rapid development of the Internet has led to a proliferation of network attacks. Therefore, to design the distributed optimization algorithm, it is necessary to consider the ability to protect the privacy information of agents in the face of malicious attacks. In this paper, a distributed optimization algorithm based on state decomposition for fixed directed graphs is proposed. Firstly, in each iteration, the algorithm updates not only the estimate of the optimal decision variable but also an auxiliary variable that estimates the average gradient of the agent's objective function. The algorithm convergence to the optimal solution of the distributed optimization problem is also discussed. Furthermore, through the state decomposition, the algorithm ensures that the gradient information of any agent cannot be precisely inferred in the presence of external eavesdroppers. Simulation results show the effectiveness of the proposed algorithm.